Small time-periodic solutions to a nonlinear equation of a vibrating string

Eduard Feireisl

Aplikace matematiky (1987)

  • Volume: 32, Issue: 6, page 480-490
  • ISSN: 0862-7940

Abstract

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In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.

How to cite

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Feireisl, Eduard. "Small time-periodic solutions to a nonlinear equation of a vibrating string." Aplikace matematiky 32.6 (1987): 480-490. <http://eudml.org/doc/15517>.

@article{Feireisl1987,
abstract = {In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.},
author = {Feireisl, Eduard},
journal = {Aplikace matematiky},
keywords = {nonlinear string equation; accelerated convergence; existence; periodic; Dirichlet boundary conditions; vibrations; damped extensive string; time-periodic solution; nonlinear string equation; accelerated convergence; existence; periodic; Dirichlet boundary conditions; vibrations; damped extensive string},
language = {eng},
number = {6},
pages = {480-490},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Small time-periodic solutions to a nonlinear equation of a vibrating string},
url = {http://eudml.org/doc/15517},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Feireisl, Eduard
TI - Small time-periodic solutions to a nonlinear equation of a vibrating string
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 6
SP - 480
EP - 490
AB - In this paper, the system consisting of two nonlinear equations is studied. The former is hyperbolic with a dissipative term and the latter is elliptic. In a special case, the system reduces to the approximate model for the damped transversal vibrations of a string proposed by G. F. Carrier and R. Narasimha. Taking advantage of accelerated convergence methods, the existence of at least one time-periodic solution is stated on condition that the right-hand side of the system is sufficiently small.
LA - eng
KW - nonlinear string equation; accelerated convergence; existence; periodic; Dirichlet boundary conditions; vibrations; damped extensive string; time-periodic solution; nonlinear string equation; accelerated convergence; existence; periodic; Dirichlet boundary conditions; vibrations; damped extensive string
UR - http://eudml.org/doc/15517
ER -

References

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  1. R. W. Dickey, 10.1137/0119019, Siam J. Appl. Math. 19 (1970), pp. 208-214. (1970) Zbl0233.34014MR0265654DOI10.1137/0119019
  2. S. Klainerman, 10.1002/cpa.3160330104, Comm. Pure Appl. Math. 33 (1980), pp. 43--101. (1980) Zbl0405.35056MR0544044DOI10.1002/cpa.3160330104
  3. P. Krejčí, Hard Implicit Function Theorem and Small periodic solutions to partial differential equations, Comment. Math. Univ. Carolinae 25 (1984), pp. 519-536. (1984) MR0775567
  4. J. Moser, A rapidly-convergent iteration method and nonlinear differential equations, Ann. Scuola Norm. Sup. Pisa 20-3 (1966), pp. 265-315, 499-535. (1966) 
  5. O. Vejvoda, et al., Partial differential equations: Time-periodic Solutions, Martinus Nijhoff Publ., 1982. (1982) Zbl0501.35001

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